1. a. Prove (without MATLAB) that (AB) -1 = B -1 A -1 using the associative law

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Question

1. a. Prove (without MATLAB) that (AB)-1 = B-1A-1 using the associative law of matrix multiplication. Hint: multiply the right-hand side of the equation by the inverse of the left-hand side of the equation.

b. Validate the above identity numerically (with MATLAB) with your choice of any two suitable 5-by-5 matrices using the following steps:

1.b.1) verify that your chosen matrices are invertible by showing all their columns are linearly independent vectors.

1.b.2) evaluate both sides of the equation above with your matrices.

1.b.3) find the sum of squared difference (error) between results of both sides of the equation to ensure accuracy.

1.b.4) produce the 5-by-5 identity matrix by multiplying AB by its inverse.

Explanation / Answer

Input Arguments

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A — Left Array
scalar | vector | matrix

Left Array, specified as a scalar, vector, or matrix. For nonscalar inputs, the number of columns in A must be equal to the number of rows in B.

B — Right Array
scalar | vector | matrix

Right Array, specified as a scalar, vector, or matrix. For nonscalar inputs, the number of columns in A must be equal to the number of rows in B.

Output Arguments

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C — Product Array
scalar | vector | matrix

Product Array, returned as a scalar, vector, or matrix. Array C has the same number of rows as input A and the same number of columns as input B. For example, if A is an m-by-0 empty matrix and B is a 0-by-n empty matrix, then A*B is an m-by-n matrix of zeros.

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1. a. Prove (without MATLAB) that (AB) -1 = B -1 A -1 using the associative law

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